32.6.15 problem Exercise 12.15, page 103

Internal problem ID [5880]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.15, page 103
Date solved : Monday, January 27, 2025 at 01:23:37 PM
CAS classification : [_separable]

\begin{align*} 2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

dsolve((2*y(x)-x*y(x)*ln(x))-2*x*ln(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x}{2}} \ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 22

DSolve[(2*y[x]-x*y[x]*Log[x])-2*x*Log[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-x/2} \log (x) \\ y(x)\to 0 \\ \end{align*}